Under the overhaul, traditional A* to G grades are being gradually replaced in England with a 9 to 1 system.

English and maths - key GCSEs for all teenagers - are the first to move across, with other subjects following over the next two years.

Among 16-year-olds in England, around 18,600 maths entries scored a 9 - the new highest grade - while almost 31,000 achieved the top mark in the two English GCSEs combined.

Geoff Barton, general secretary of the Association of School and College Leaders, said teachers and pupils had “performed miracles” in “very challenging circumstances”.

Statistics published by the Joint Council for Qualifications (JCQ) show that in England:

* In maths, 3.5% of entries - around 18,617 in total - scored a 9

* In English, 2.6% of entries - around 13,754 - scored a 9

* In English literature, 3.3% - around 17,187 - scored a 9

* Girls secured around two-thirds of the 9 grades

Fewer candidates achieved a 9 than the proportion who gained an A* under the traditional A*-G grading system, following the deliberate move to change the system to allow more differentiation, particularly between the brightest candidates.

There are now three top grades - 7, 8 and 9 - compared with two under the old system - A* and A - with A* results now split into 8s and 9s.

The grading switch is part of wider reforms designed to make GCSEs more rigorous and challenging.

Maths in particular has more content, and in both subjects there has been a move away from coursework and pupils now sit all exams at the end of the two-year courses, rather than throughout.

Although the exams have been made more demanding, broadly the same proportions of candidates have achieved key passes - such as at the A/7 boundary, due to processes put in place to ensure that results are comparable and that students taking the first new courses are not disadvantaged.

Data published by exams regulator Ofqual shows that among 16-year-olds in England, 19.9% of maths entries were awarded at least a 7 or higher this year, similar to 2016 when 20% achieved an A or A*.

In English language, 16.8% scored at least a 7, compared with 16.2% who gained at least an A last year, while in English literature, 19.1% achieved between 7 and 9, compared with 21.1% of A-A* grades last year.

Mr Barton said: “Congratulations to the pupils and their teachers on this year’s GCSE results which have been achieved in very challenging circumstances. They have performed miracles amidst a sea of curriculum change which continues unabated next year. They deserve tremendous credit for their hard work.”

“We have used the same tried and tested principle of comparable outcomes, as in previous years, to ensure that this first cohort of students is not disadvantaged.

“If a student receives a grade 7 today, they could have expected to have received a grade A last year.

“And if they get a grade 4, they could have expected to get a grade C in 2016.”

Pupils needed fifth of marks for standard pass in new maths GCSE

Students needed just under a fifth of marks in this year’s higher-level maths GCSE to achieve a grade 4, considered a standard pass, figures show.

Getting just over half the marks gave candidates a new grade 7 - equivalent to an A - while those scoring at least 79% were awarded a 9 - the highest result under England’s new 9-1 grading system.

Students in England are the first to receive numerical grades having taken new, tougher exams in English and maths.

In general, after moves to make the courses more demanding and changes to the structure - such as ditching coursework and pupils taking exams at the end of the two-year course, rather than throughout - there has been movement of just a couple of percentage points in the proportions of students achieving key grades, such as at grade 4, broadly equivalent to the traditional C grade.

This year, 70.7% of 16-year-olds in England gained a 4 or higher in maths, compared with 71.4% who achieved at least a C last year, while in English language, 69.7% got a 4 or higher compared with 69.7% getting A*-C last year, and in English literature 72.5% got a 4 or higher, compared with 74.6% gaining at least a C last year.

There were significantly higher numbers of pupils taking English GCSEs this year, amid a move away from international GCSEs and changes to what counts in annual school performance tables.

Figures published by Ofqual show that students sitting the higher tier maths GCSE needed to score at least 18% on average to secure a grade 4, while 52% was the boundary for a 7 on average, and 79% was the average required for a grade 9.

On the higher tier paper, 4 is understood to be the lowest grade possible, with half of the marks in the exam targeted at grades 4-6 and the other half at grades 7-9.

Professor Alan Smithers, director of the Centre for Education and Employment Research at Buckingham University, said grade boundaries had been dropped this year to ensure that sufficient students achieved key results.

“What has happened this year is the regulator has penned the new grade 7 to an A grade and the new grade 4 to a C grade,” he said.

“In order to maintain that, it’s dropped the number of marks required for a pass at various levels. In some cases, it’s dropped them very low, it’s more or less giving away the grade.

“Ofqual maintains this is necessary to maintain standards across the years, but in fact it is taking away some of the point of the exams, which is to enable users of the results to tell people apart with greater accuracy.”

Exams regulator Ofqual has had processes in place for some years to ensure that results are comparable each year, which are also intended to ensure that students taking the first new courses this summer are not disadvantaged.

An Ofqual spokesman said: “The higher tier paper caters for students who might be looking to achieve a grade 4 right up to a grade 9. It starts with grade 4 level questions.

“In contrast, the foundation tier paper caters for students seeking to achieve a grade 1 through to grade 5. The different grade boundaries on the two papers reflect that.

“These boundaries were set using a combination of statistics and examiner judgment. We are confident that they reflect an appropriate standard of performance.”